Stable Mixing in Hawk-Dove Games under Best Experienced Payoff Dynamics

The hawk-dove game admits two types of equilibria: an asymmetric pure equilibrium, in which players in one population play - hawk and players in the other population play dove and an inefficient symmetric mixed equilibrium, in which hawks are frequently matched against each other. The existing literature shows that populations will converge to playing one of the pure equilibria from almost any initial state. By contrast, we show that plausible dynamics, in which agents occasionally revise their actions based on the payoffs obtained in a few past interactions, can give rise to the opposite result: convergence to one of the interior stationary states.
*This paper contains some parts of an unpublished working paper titled “Sampling Dynamics and Stable Mixing in Hawk–Dove Games.” The authors thank Augusto Santos and Amnon Schreiber for various
helpful comments and suggestions.